Bounds for short covering codes and reactive tabu search Original Research Article

Given a prime power image, image denotes the minimum cardinality of a subset image in image such that every word in this space differs in at most image coordinates from a multiple of a vector in image. In this work, two new classes of short coverings are established. As an application, a new optimal record-breaking result on the classical covering code is obtained by using short covering. We also reformulate the numbers image in terms of dominating set on graphs. Departing from this reformulation, the reactive tabu search (a variation of tabu search heuristics) is developed to obtain new upper bounds on image. The algorithm is described and conclusions on the results are drawn; they identify the advantages of using the reactive mechanism for this problem. Tables of lower and upper bounds on image, image, image, and image, are also presented.